At the top, kinetic energy is 0 since it starts at rest. At the bottom we choose the potential to be zero
So using conservation,
[tex] mgz= \frac{1}{2}m\vec{v_f}^2[/tex]
Then, substitute [tex] z=s(t)sin\theta[/tex],
And [tex] \vec{v_f} = \vec{a}t [/tex]
where [tex] \vec{a} = \frac{\vec{F}}{m} = \frac{mgsin\theta}{m} = gsin\theta [/tex]